Internal transfer being ghosted by HR?

I work for a small hospital and applied/interviewed for an internal position with our larger parent hospital. Interview was 8/17. On 8/20 I was contacted by my HR recruiter with a verbal offer including pay/benefits/hours/orientation length. She gave me a transfer date of 9/27 and told me to inform my manager as soon as possible, which I did 8/23. I expressed my concerns of giving notice without a written offer, however HR stated this is run of the mill for internal transfers due to the paperwork that has to go through etc. I am contractually obligated to giving 4 weeks notice and she said if I wait for a formal offer letter my transfer date will end up being postponed. 

I haven’t heard anything since 8/20. I called HR 9/9, 9/10, and this morning (9/13), the receptionist looked at my file and was able to see an offer has been extended which is reassuring, however my recruiter was “on the phone” so she transferred me to her office each time to leave a voicemail, which I did. I also sent an email this afternoon. None of my calls/messages have been returned. My transfer date is 2 weeks from today and I have no written offer or any info on where or when to show up. 

If I was quitting my institution as a whole I wouldn’t sweat it and would just take the time off, however since it’s an internal transfer I am under the impression I am still obligated to 36 hrs/week regardless. I am off the schedule in 2 weeks at my current job. 

To say I’m frustrated would be an understatement. I don’t know where to go from here. The only other contact I have is the manager who emailed me, but I’m not sure if reaching out to her would be overstepping. Advice appreciated.